Suppose we cascade a differentiator and a smoother systems characterized by the following input/output equations where the
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![Differentiator w[n] = x[n] – x[n – 1] w[n] У[n — 1] Smoother y[n] = 3 3 3.](https://dsd5zvtm8ll6.cloudfront.net/si.question.images/images/question_images/1545/8/1/8/1915c23504f7063c1545800776546.jpg)
where the output of the differentiator and input to the smoother is w[n], while x[n] is the input of the differentiator (and of the overall system) and y[n] is the output of the smoother (and of the overall system).
(a) If x[n] = u[n] and the initial conditions for the smoother are zero, find the output of the overall system y[n].
(b) If x[n] = ( ˆ’ 1) n , ˆ’ˆž < n < ˆž, find the steady-state response yss [n] of the overall system yss [n].
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Let Hsz and Hz be the transfer funct...View the full answer
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